Two-nil up after a first 40 minutes that David O'Leary accepted should have brought them four or five goals, they were brought back to earth by two from Alan Shearer, but then kept their composure to win it through the previously profligate Michael Bridges.
Although they flirted with the preposterous notion of failing to take all three points, there was so much to admire in Leeds' display. And if they failed to gain their full reward, the movement and understanding between Bridges and Alan Smith was remarkable for two raw talents with only a handful of games together.
Harry Kewell was a threat wherever his free role took him, Lee Bowyer and David Batty provided the central thrust, while Eirik Bakke was a revelation on his full debut.
Until he tired in the second half, the young Norwegian found more space than anyone, set up the first goal for Bowyer and supplied educated and constructive touches all over the pitch. O'Leary also had a handy reinforcement up his sleeve in the shape of Newcastle reject Darren Huckerby, who did much to set up the winner.
O'Leary is still in the market for a proven striker to take on the mantle of Jimmy Floyd Hasselbank, but his resources must look impressive enough to Bobby Robson. Shearer has clearly rediscovered his spark - his two clinically taken goals showed Bridges what was required - but he is liable to find himself working in isolation.
Already without the company of the chronically injury-prone Duncan Ferguson, Shearer lost Temuri Ketsbaia with a knee injury towards the end of the first half. Shearer needs help if he is to maintain the momentum of his personal revival and Robson indicated that he will be asking for money to finance some assistance for him.
After the 8-0 romp against Sheffield Wednesday that kick-started their season, Newcastle always knew that this would be a very different test.
Although their defence was over-run in the first half, the Magpies showed the resilience to fight back. Apart from Shearer's rediscovered zest, Kevin Keegan, watching his old club from the stand with his England hat on, would have enjoyed the performance of Kieron Dyer.
He was a restless bundle of energy and ideas throughout. Given any sort of structure about them, he and Shearer can lead a steady climb up the table.
The youth and enterprise of O'Leary's side suggests that it is only going to get better. If it could add remorseless finishing to its many other qualities, it would be formidable already.
Goals: Bowyer (11) 1-0; Kewell (40) 2-0; Shearer (42) 2-1; Shearer (54) 2-2; Bridges (77) 3-2.
Leeds United (4-4-2): Martyn; Kelly, Radebe, Woodgate, Harte; Bakke (Haaland, 77), Batty, Bowyer, Kewell; Smith (Huckerby, 71), Bridges. Substitutes not used: Mills, Jones, Robinson (gk).
Newcastle United (4-4-2): Harper; Barton, Marcelino, Goma, Domi; Solano, McClen (Charvet, 72), Dyer, Speed; Shearer, Ketsbaia (Robinson, 43). Substitutes not used: Glass, Hughes, Wright (gk).
Referee: B.Knight (Orpington).
Bookings: Leeds: Martyn, Radebe, Kelly, Smith, Batty. Newcastle: Marcelino, Domi, Speed.
Man of the match: Bowyer.